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Simplifying 7X + 39 = (X + 3)(X + 3) Reorder the terms: 39 + 7X = (X + 3)(X + 3) Reorder the terms: 39 + 7X = (3 + X)(X + 3) Reorder the terms: 39 + 7X = (3 + X)(3 + X) Multiply (3 + X) * (3 + X) 39 + 7X = (3(3 + X) + X(3 + X)) 39 + 7X = ((3 * 3 + X * 3) + X(3 + X)) 39 + 7X = ((9 + 3X) + X(3 + X)) 39 + 7X = (9 + 3X + (3 * X + X * X)) 39 + 7X = (9 + 3X + (3X + X2)) Combine like terms: 3X + 3X = 6X 39 + 7X = (9 + 6X + X2) Solving 39 + 7X = 9 + 6X + X2 Solving for variable 'X'. Reorder the terms: 39 + -9 + 7X + -6X + -1X2 = 9 + 6X + X2 + -9 + -6X + -1X2 Combine like terms: 39 + -9 = 30 30 + 7X + -6X + -1X2 = 9 + 6X + X2 + -9 + -6X + -1X2 Combine like terms: 7X + -6X = 1X 30 + 1X + -1X2 = 9 + 6X + X2 + -9 + -6X + -1X2 Reorder the terms: 30 + 1X + -1X2 = 9 + -9 + 6X + -6X + X2 + -1X2 Combine like terms: 9 + -9 = 0 30 + 1X + -1X2 = 0 + 6X + -6X + X2 + -1X2 30 + 1X + -1X2 = 6X + -6X + X2 + -1X2 Combine like terms: 6X + -6X = 0 30 + 1X + -1X2 = 0 + X2 + -1X2 30 + 1X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 30 + 1X + -1X2 = 0 Factor a trinomial. (6 + -1X)(5 + X) = 0Subproblem 1
Set the factor '(6 + -1X)' equal to zero and attempt to solve: Simplifying 6 + -1X = 0 Solving 6 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1X = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1X = 0 + -6 -1X = 0 + -6 Combine like terms: 0 + -6 = -6 -1X = -6 Divide each side by '-1'. X = 6 Simplifying X = 6Subproblem 2
Set the factor '(5 + X)' equal to zero and attempt to solve: Simplifying 5 + X = 0 Solving 5 + X = 0 Move all terms containing X to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + X = 0 + -5 Combine like terms: 5 + -5 = 0 0 + X = 0 + -5 X = 0 + -5 Combine like terms: 0 + -5 = -5 X = -5 Simplifying X = -5Solution
X = {6, -5}
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